What is Ohm's law?

Ohm's law describes the relationship between voltage, current and resistance in an ohmic component under constant physical conditions. Its basic expression is V = I × R. Georg Simon Ohm published this relationship in his 1827 work.

With resistance held constant, current increases in proportion to voltage. With voltage held constant, increasing resistance reduces current. This relationship helps explain wiring losses and supports everyday electronic circuit calculations.

Equations, symbols and units

V is voltage, measured in volts (V); I is current, measured in amperes (A); and R is resistance, measured in ohms (Ω). Some references use U for voltage.

Voltage: V = I × R
Current: I = V / R
Resistance: R = V / I

Convert units before calculating: 1 kΩ = 1000 Ω and 1 mA = 0.001 A. For example, 12 V across 2 kΩ produces 0.006 A = 6 mA. Voltage and current are different quantities; volts and amperes cannot be used interchangeably.

Three worked examples

Current: A 48 Ω resistor connected to 24 V carries I = 24 / 48 = 0.5 A. Increasing resistance to 96 Ω at the same voltage reduces current to 0.25 A.

Voltage: If 20 mA flows through 100 Ω, first convert 20 mA to 0.020 A. The voltage is V = 0.020 × 100 = 2 V.

Resistance: If a load has 12 V across it and carries 0.2 A, the ratio at that operating point is V / I = 60 Ω. One measurement does not establish that the load behaves as a constant 60 Ω resistor at every voltage.

Power: Resistance alone is not enough

Electrical power is calculated using P = V × I. For an ohmic resistor, equivalent forms are P = I² × R and P = V² / R. The 24 V, 48 Ω example dissipates 12 W.

A 48 Ω resistor rated at 0.25 W cannot continuously handle this load. Select a load resistor using its power rating, ambient temperature, mounting requirements and manufacturer derating conditions. Doubling voltage across a constant resistance doubles current and increases power by a factor of four.

Series and parallel resistance

In a series circuit, the same current flows through every resistor and Rtotal = R1 + R2 + .... A 10 Ω resistor and a 20 Ω resistor in series total 30 Ω. At 12 V, current is 0.4 A and the voltage drops are 4 V and 8 V.

In a parallel circuit, every branch has the same voltage. Use 1 / Rtotal = 1 / R1 + 1 / R2 + .... Two 100 Ω resistors in parallel total 50 Ω. At 12 V, each branch carries 0.12 A, giving 0.24 A in total.

Practical uses in the field

Connection losses: A loose connection carrying 5 A with 0.2 Ω of contact resistance produces a 1 V drop and 5 W of heating. Assessing voltage drop requires checking the connection under load as well as the supply itself.

LED resistor: For an LED with a 2 V forward voltage and a target current of 10 mA on a 12 V supply, the series resistance is approximately R = (12 − 2) / 0.010 = 1000 Ω. Resistor dissipation is 0.1 W. Diode forward-voltage variation and supply tolerance affect the final selection.

Analog measurements: A 4–20 mA signal develops 1–5 V across a suitable precision 250 Ω resistor. Check the PLC input specifications, transmitter load capability and total loop resistance. A 250 Ω resistor cannot be added unconditionally to every system.

Does the same calculation apply to every device?

The constant-resistance assumption matters. Transistors, diodes and LEDs behave nonlinearly. An incandescent lamp's resistance changes as it heats up. Dividing a device's rated voltage by an arbitrary measured resistance does not reliably predict its operating current.

Ohm's law also applies to a pure resistance supplied with AC; RMS values can be used for sinusoidal signals. AC circuits containing capacitors and inductors involve frequency-dependent impedance and phase relationships. The simple constant-resistance model used for DC cannot be applied to every AC load.

Measuring safely and accurately

Measure resistance with a multimeter only on a de-energised circuit. Verify that power is off and that capacitors have been safely discharged. Parallel paths may affect the reading; disconnect one component terminal when necessary.

Measure voltage in parallel and current in series using a suitable ammeter or multimeter. Connecting probes in the current input directly across a supply can cause a short circuit. An oscilloscope can reveal rapid changes, but its connections and measurement limits must also be checked.